OVERALL
I appreciate the effort that Dr. Gasparini and co-authors placed in this revision. I heartily agree with her/their assessment that the community would be helped by model intercomparison and better benchmarking, to ensure that we are all "speaking the same language" when discussing how these models work.
I found myself quite interested in the questions that this revised paper raised. With the self-awareness that I might be a bit looser around tradition, I find it quite okay that this paper focuses on just a question without resolving it. While such resoloutions are nice, demonstrating this multi-layered discrepancy in response times within very simple models that are so commonly used seems quite important to do. Indeed, while my typical mode would be to hunt down the solution myself, perhaps publishing this sooner would help the broader LEM commmunity to address the multi-faceted problem of response times, nonlinear responses, and benchmarking.
I close with an apology for my delay in submitting this review.
Andy Wickert
Somewhere over the Atlantic
2024.03.01
GENERAL
I am very interested in the finding that drainage rearrangement drives the longer-than-theoretical and inconsistent landscape response times. I comment on this a bit more below, but I have a couple of thoughts regarding possibliities. I am not sure if you will find them in-scope or out-of-scope, and leave this for the authors to decide.
First, I thought of Kwang et al. (2021), who note that the lateral dynamics of rivers can be quite important in sustaining a dynamic, rather than static, equliibrium topography. Do you think that "noise" in erosion rates caused by this process could further delay the approach to equilibrium beyond the Whipple & Tucker (1999) analytical calculation? This might further underscore your point towards the end of the article: even though the lateral-erosion component is not included in your tested LEMs, adding more expected realism might further separate from the theory rather than making the model closer. What do you think?
*Note that I was Jeffrey Kwang's postdoc advisor and a graduate-student colleague with his co-author Abby Langston. Please do not feel any pressure to cite this work; there may be other papers out there, and I just know this one.*
Second, I considered how drianage basins form in the first place, as the Whipple & Tucker (1999) theoretical predction is based on the idea that the channel already exists. However, we see that the initial integration of drainage networks can produce lags in landscape evolution (cf. Lai & Anders, 2018: in this case, even when flow across internal depressions is allowed).
I then wondered about the more fundamental difference between propagation of a signal up an existing river and catchment (what Whipple & Tucker, 1999, were considering for "response time") and the time it takes for that order to co-develop alongside the signal propagation (what you are measuring in the models, albeit, with the additional consideration of what the models themselves are doing). This is all quite interesting, to me, in two specific ways. First, it lines up with some recent work demonstrating that cross-basin draingae integration may likely occur via overflow events (Hilgendorf et al., 2020) and that headward erosion is unlikely unless a channel already exists. Second, it underscores that we may have "noise" in how real landscapes respond to perturbations because of the nonlinear interactions of drainage sub-basins playing out atop whatever initial conditions existed, potentially giving both limit and geological guidance to geomorphic predictions.
[minor] The article is 342 lines of text+equations, with three large figures and one table. I checked the definition of "short communication" and confirmed my memory that this manuscript type should be "a few pages only". I would see it as a considerable overstep of my role here to discuss which kind of manuscript it *should* be, but I want to point this out to the editors and authors.
https://www.earth-surface-dynamics.net/about/manuscript_types.html
LINE BY LINE
7
"The sensitivity of time to steady state to computational time step is not consistent among models or even within a single model."
The 2x "to" make the meaning ambiguous. I suggest:
"Time to steady state varies inconsistently with time-step length, both within a single model and among different models."
Is that right? I hope so. Otherwise I really didn't understand.
95 (and other equations)
[minor] I think that ESurf has commas or other punctuation after equations, such that they fit into the surrounding sentence structure
106
timesteps --> time-step lengths?
132 (& hereafter)
[typographical]
1e-4 to $10^{-4}$ (imagine it being typeset) and so on
133
Because you are discussing the workings of LEMs, might it be useful to consider the findings of Kwang & Parker (2017), that fluvial-only LEM outputs are scale invariant with m/n=0.5? I am wondering if this might be generally helpful when discussing the applicability of your results: despite your careful consideration of standardized initial conditions, you have also picked a parameter set that should be scale invariant.
136 (Eq. 3)
Could you pull the "v" outside of the differential operator?
Alternatively, you could change the "d"s to "\Delta"s, which would make this become a fraction instead of an operator.
150-160
[self-narration; no response needed]
I am anxious about how the stability of your time steps might relate to your findings here, especially because only a subset of the models tested will be used for certain time steps. Because of how drainage-area changes can affect knickpoint celerity, and drainage-capture events can occur instantaneously, I am likewise wondering if this could turn into the major time-step dependence. I'm continuing to read with this in mind.
152-153
Inline citation; consider "shown by"
183 (& following)
Why "100,000"? And this is presumably years. It feels arbitrary, so a small note could help.
190
Could this more precisely be called "maximum temporal change in elevation" (as opposed to "temporal change in maximum elevation")? Then the English would follow the math closely.
195
A pair of nitpicks, one more real and one more convention.
The more "real" one is that dissolved, colloidal, etc. load are not considered to be "sediment". Therefore, perhaps you could consider noting the temporal change in total material removed from the landscape. This says what you are going for while removing the implicit assumption that eroded material becomes sediment.
Second, "flux" is mathematically and traditionally used as the transfer of a quantity across a plane, such that its units are [thing]/[area*time]. This is not how the sedimentologits & al. use it, or the climate scientists. So that's why this is a nitpick.
214-218 (please ignore; including for narrative of my thinking during the review process)
This threshold seems arbitrary. Might it be better to consider a time scale that emerges naturally from the model outputs, e.g., finding an exponential decay time scale and defining some multiple of this?
On second thought, I scrolled down to your plots. I suppose they aren't all that exponential!
224 (Eq. 10)
Could you define "L"? (I've double-checked and hope I'm not just missing it!) I'm guessing that it is some kind of length scale -- perhaps half of the domain width?
Table 1 + Figure 1: This is a small thing, but I wonder if you could place the experiments within both of these in the same order. It would help in interpreting the results.
Figure 3: Some dangling text has been left in the caption at the end.
334-335 (also a bit of my own thinking, use/don't use at will)
I agree about this being the minimum response time, as (with your above note) the channels might not until later extend all the way up to the drainage divide with a steady-state basin area. I think that one other implication of this important point (though perhaps also beyond the scope of your article here) is the oft-invoked but seemingly mythical beast of channel headward propagation, used often in arguments of drainage integration. Knickpoints can propagate quickly upstream, but rearranging the channel head where drainage area --> 0 can be quite slow.
REFERENCES
Hilgendorf, Z., Wells, G., Larson, P. H., Millett, J., & Kohout, M. (2020). From basins to rivers: Understanding the revitalization and significance of top-down drainage integration mechanisms in drainage basin evolution. Geomorphology, 352, 107020. https://doi.org/10.1016/j.geomorph.2019.107020
Kwang, J. S., Langston, A. L., & Parker, G. (2021). The role of lateral erosion in the evolution of nondendritic drainage networks to dendricity and the persistence of dynamic networks. Proceedings of the National Academy of Sciences, 118(16), e2015770118. https://doi.org/10.1073/pnas.2015770118
Kwang, J. S., & Parker, G. (2017). Landscape evolution models using the stream power incision model show unrealistic behavior when m∕ n equals 0.5. Earth Surface Dynamics, 5(4), 807-820.
Lai, J., & Anders, A. M. (2018). Modeled Postglacial Landscape Evolution at the Southern Margin of the Laurentide Ice Sheet: Hydrological Connection of Uplands Controls the Pace and Style of Fluvial Network Expansion. Journal of Geophysical Research: Earth Surface, 123(5), 967–984. https://doi.org/10.1029/2017JF004509 |
